Algebra worksheet — GCSE Foundation

1.A curve has equation y = x² − 9. Which statement about its graph is correct?

2.Make x the subject of the formula y = 5x + 3.

3.A car passes the 15 km marker on a road and passes the 195 km marker 3 hours later. Work out the gradient of the distance-time graph, that is the rate of change of distance with time.

4.The diagram shows a distance–time graph for a cyclist travelling at a constant speed, for the first 6 minutes of a journey. Distance is in kilometres and time is in minutes. Work out how far the cyclist would travel in 20 minutes at the same speed.

5.Here are the first five terms of an arithmetic sequence: 4, 7, 10, 13, 16. Work out the 9th term.

6.A number machine adds 1 to its input. Isla says that an input of 5 gives an output of 6. Which statement is correct?

7.Write down the coordinates of the point where the line y = 2x + 4 crosses the y-axis.

8.In a sequence, each term is half the term before it. The sequence begins 100, 50, 25. Write down the next term.

9.The first four terms of a sequence are 11, 18, 25, 32. Ravi thinks the nth term is 7n. Work out the correct expression for the nth term.

10.The solution to an inequality is n ≤ 5. Write down the largest integer value of n that satisfies this inequality.

11.Which of these equations gives a graph with two separate curved branches — one where x and y are both positive, and one where x and y are both negative?

12.A sequence has the position-to-term rule: the term is the square of the position number. Its first four terms are 1, 4, 9, 16. Work out the 10th term.

13.Here are the first four terms of an arithmetic sequence: 5, 9, 13, 17. Work out the 5th term.

14.A theatre's front row has 18 seats. Each row behind has 4 more seats than the row in front. Which row has exactly 62 seats?

15.A Fibonacci-type sequence begins 3, 5, 8, 13, ... where each term after the second is the sum of the two terms before it. Work out the 7th term of the sequence.